boxplot: Boxplot of the Residuals

The option of plots = "boxplot" creates a boxplot of the residuals.

This can be used to visualize the distribution of the residuals from the model. It may help to identify outliers or determine if the distribution of the residuals is skewed.

# Creates a boxplot of the residuals
resid_panel(tree_model, plots = "boxplot")

cookd: Cook’s Distance Plot

The option of plots = "cookd" creates a plot of the Cook’s distance values versus the observation numbers. It is only available for “lm” and “glm” models. The blue dashed horizontal line is placed at 4/n where n is the number of observations used to fit the model (Rawlings, Pantula, and Dickey 1998).

This plot can be used to check for points with high leverage. Points above the dashed blue line are considered to be high leverage points, and points that have Cook’s D values that are much larger than the rest are of particular interest.

# Creates a Cook's D plot
resid_panel(tree_model, plots = "cookd")

hist: Histogram of the Residuals

The option of plots = "hist" creates a histogram of the residuals. The blue line is a normal density curve with a mean of zero and a standard deviation equal to the standard deviation of the residuals.

resid_panel includes a bins option to specify the number of bins in the histogram. By default, bins = 30 is based on the default for the number of bins in the ggplot2 geom_histogram function.

This is another plot that can be used to visualize the distribution of the residuals. In particular, the normal density curve allows for the comparison of the residuals to a normal distribution.

# Creates a histogram of the residuals
resid_panel(tree_model, plots = "hist")

# Creates a histogram with 20 bins
resid_panel(tree_model, plots = "hist", bins = 20)

index: Index Plot of the Residuals

The option of plots = "index" creates a plot of the residuals versus the observation numbers. A solid blue horizontal line through 0 is included for reference.

resid_panel includes a smoother indicator option. If set to TRUE, a loess smoother will included on the index plot as a red solid line. If set to FALSE, it will not be included. By default, smoother = FALSE. (This option also affects the lev, ls, and resid plots.)

This plot can be used to look for patterns in the residuals in regards to the order of the data used to fit the model. Often the data are ordered in a meaningful way such as by time of observation. This plot can help to check if there is any relationship between the residuals and the order of the data. If a trend is found in this plot, it may suggest that a variable has been excluded from the model that would help to explain the variation in the response variable.

# Creates an index plot of the residuals
resid_panel(tree_model, plots = "index")

# Creates an index plot with a smoother added
resid_panel(tree_model, plots = "index", smoother = TRUE)

lev: Residual-Leverage Plot

The option of plots = "lev" creates a plot of the standardized residuals versus the leverage values. This plot is only available for “lm” and “glm” models. A horizontal line through 0 and a vertical line through 0 are included as black dashed lines to mimic the residual-leverage plot created by the plot.lm function from base R. The red dashed lines are Cook’s distance contour lines for Cook’s D values of 0.5 and 1. These values were chosen based on the default options used in plot.lm.

The smoother option in resid_panel also affects the location-scale plot. If set to TRUE, a loess smoother will be included on the residual-leverage plot as a red solid line. If set to FALSE, it will not be included. By default, smoother = FALSE. (This option also affects the index, ls, and resid plots.)

The Cook’s D contour lines are computed using the fact that Cook’s distance can be written as a function of the leverage and the standardized residual. For observation \(i\), let \(D_i\) represent the Cook’s distance, \(r_i\) represent the standardized residual, and \(h_i\) represent the leverage value. Finally, let \(p\) be the rank of the model. Cook’s distance can be computed as \[D_i = \frac{r^2_i}{p}\left(\frac{h_i}{1-h_i}\right).\] (Seber and Lee 2003). Thus, given a specified value of Cook’s D, a leverage value (\(h_i\)), and the rank of the model (\(p\)), it is possible to solve for the value of the standardized residual (\(r_i\)). The value of \(D_i=1\) is used since a data point with a value of Cook’s D larger than 1 is often considered to be a point with high leverage (Chatterjee and Hadi 2012).

This plot can be used to look for trends in the residuals based on the leverage values and to identify points with high leverage. Points that fall outside of the Cook’s D contour lines may be of interest. Points that fall outside of either contour line with Cook’s D set to 1 are considered to be high leverage points. As seen in the plot below, not all contour lines may appear when the plot is created if they fall far outside of the range of the observed leverage values.

# Creates a residual-leverage plot
resid_panel(tree_model, plots = "lev")

# Creates a residual-leverage plot with a smoother added
resid_panel(tree_model, plots = "lev", smoother = TRUE)

ls: Location-Scale Plot

The option of plots = "ls" creates a location-scale plot of the residuals. This plot is only available for “lm” and “glm” models. It plots the square root of the absolute value of the standardized residuals on the y-axis and the predicted values on the x-axis. The predicted values are plotted on the original scale for “glm” and “glmer” models.

The smoother option in resid_panel affects the appearance pf the location-scale plot. If set to TRUE, a loess smoother will be included on the location-scale plot as a red solid line. If set to FALSE, it will not be included. By default, smoother = FALSE. (This option also affects the index, lev, and resid plots.)

The location-scale plot can be used to check for patterns in the residuals in relationship to the predicted values. For example, homogeneity of the residuals can be diagnosed by determining whether the residuals show equal spread along the range of the predicted values. In the ideal situation, the loess curve would be a straight line with points evenly dispersed around it for the whole range of the predicted values.

# Creates a location-scale plot of the residuals
resid_panel(tree_model, plots = "ls")

# Creates a location-scale plot of the residuals with a smoother added 
resid_panel(tree_model, plots = "ls", smoother = TRUE)

qq: Normal Quantile Plot

The option of plots = "qq" creates a normal quantile plot of residuals using the R package qqplotr. The sample quantiles are plotted on the y-axis, and the theoretical normal quantiles are plotted on the x-axis. See the qqplotr documentation for details on the computation of the sample and theoretical quantiles. The blue line is a 1-1 line shown for reference.

resid_panel includes two options to adjust the normal quantile plot based on the qqplotr package. The option of qqline indicates whether to include the 1-1 line on the qq-plot. By default, qqline = TRUE. The option of qqbands indicates whether to include 95% confidence bands on the qq-plot. By default, qqbands = FALSE.

This plot is meant to be used to check if the residuals approximately follow a normal distribution. If the points follow the 1-1 line, it suggests that the residuals are approximately normally distributed.

# Creates a normal quantile plot of the residuals
resid_panel(tree_model, plots = "qq")

# Creates a qq-plot with the 1-1 line removed
resid_panel(tree_model, plots = "qq", qqline = FALSE)

# Creates a qq-plot with the confidence bands added
resid_panel(tree_model, plots = "qq", qqbands = TRUE)

resid: Residual Plot

The option of plots = "resid" creates a plot of the residuals versus the predicted values. The predicted values are plotted on the original scale for “glm” and “glmer” models. A solid blue horizontal line through 0 is included for reference.

The smoother option in the resid_panel function can add a smoother to this plot. If set to TRUE, a loess smoother will be included on the residual plot as a red solid line. If set to FALSE, it will not be included. By default, smoother = FALSE. (This option also affects the index, lev, and ls plots.)

The residual plot can be used to check for homogeneity (constant variance) of the residuals and possible violations of the linearity assumption. The assumption of homogeneity is met if the residuals have approximately the same variance throughout the entire range of the predicted values. The assumption of linearity may be violated if there is some trend in the residuals so that the residuals are not evenly distributed below and above 0 throughout the range of the predicted values.

# Creates a residual plot
resid_panel(tree_model, plots = "resid")

# Creates a plot with the smoother added
resid_panel(tree_model, plots = "resid", smoother = TRUE)

yvp: Response vs. Predicted Plot

The option of plots = "yvp" creates a plot of the observed response variable values versus the predicted values from the model. Both response variable and predicted values are plotted on the original scale for “glm” and “glmer” models. The blue solid line is a 1-1 line, which is included for reference.

This plot provides a visualization to assess how similar the model predictions of the response variable are in relationship to the observed response variable values. The model is producing predictions similar to the observed values if the points follow the 1-1 line.

# Creates a plot of observed values vs. fitted values
resid_panel(tree_model, plots = "yvp")

all: Panel of All Plots

The option of plots = "all" creates a panel of all plots included in the package that are available for the type of model input into resid_panel. Note that “cookd”, “ls”, and “lev” are not available for “lmer”, “lmerTest”, “glmer”, and “lme” models.

# Creates a panel of all plots available for an "lm" model
resid_panel(tree_model, plots = "all")

default: Default Panel

Unsurprisingly, the option of plots = "default" is the default panel displayed when resid_panel is applied to a model with no plots option specified. This creates a panel with a residual plot, a normal quantile plot of the residuals, an index plot of the residuals, and a histogram of the residuals.

# Creates the default panel of plots
resid_panel(tree_model)

# Creates the default panel with the option explicitly specified
resid_panel(tree_model, plots = "default")

R: Base R Inspired Panel of Plots

The option of plots = "R" is designed to mimic the diagnostic plots created by applying the base R function plot to an “lm” or “glm” model. As a result, it can only be used with an “lm” or “glm” model. It creates a panel with a residual plot, a normal quantile plot of the residuals, a location-scale plot, and a residual-leverage plot.

# Creates the R panel of plots with the smoother option set to TRUE
resid_panel(tree_model, plots = "R", smoother = TRUE)

# These are the lm diagnostic plots from base R which the "R" panel is designed to mimic
par(mfrow = c(2,2)) # Creates a 2x2 grid of plots
plot(tree_model)    # Creates the base R diagnostic plots

par(mfrow = c(1,1)) # Returns the settings to a 1x1 grid of plots

SAS: SAS Inspired Panel of Plots

The option of plots = "SAS" creates a panel with a residual plot, a normal quantile plot of the residuals, a histogram of the residuals, and a boxplot of the residuals. This was modeled after the residpanel option in proc mixed from SAS.

# Creates the SAS panel of plots
resid_panel(tree_model, plots = "SAS")

boxplot: Boxplot of the Residuals

The option plots = "boxplot" creates an interactive boxplot. If the cursor is hovered over the vertical line created by the whiskers in the plot, a tooltip appears at the location of each of the residual points. (Note that the points are not visible on the plot.) The tooltip lists the value of the residual, and the remaining information lists the variables included in the model with the observed value and the observation number of the point. If the cursor is hovered anywhere else on the boxplot, tooltips will appear showing the location and value of the minimum, maximum, median, and first and third quantiles of the residuals.

# Creates an interactive boxplot of the residuals
resid_interact(tree_model, plots = "boxplot")

cookd: Cook’s Distance Plot

The option plots = "cookd" creates an interactive Cook’s distance plot. When the cursor is hovered over a point, a tooltip is displayed. It lists the Cook’s D value for that point as well as the observed data values and observation number. This plot is only available for “lm” and “glm” models.

# Creates an interactive Cook's D plot
resid_interact(tree_model, plots = "cookd")

hist: Histogram of the Residuals

The option of plots = "hist" creates an interactive histogram of the residuals. The cursor can be hovered over the bars in the histogram to display a tooltip that lists the density value at the top of the bar and the number of observations in the bar (“count”). If the cursor is hovered over the bottom of the plot where the density is equal to 0, a tooltip appears that shows the location of the data points and lists the observed variable values and the observation number of the data point.

resid_interact includes the same bins option as resid_panel for the histogram. It allows the user to specify the number of bins to use when creating the histogram. Again, by default, bins = 30.

# Creates an interactive histogram of the residuals
resid_interact(tree_model, plots = "hist")

# Creates an interactive histogram with 20 bins
resid_interact(tree_model, plots = "hist", bins = 20)

index: Index Plot of the Residuals

The option of plots = "index" creates an interactive index plot of the residuals. The cursor can be hovered over a data point to see a tooltip that contains the observation number of the point, the value of the residual, and the observed variable values.

resid_interact also includes the smoother option for the index plot which indicates whether or not to include a loess smoother on the index plot. Set smoother = TRUE to have the smoother appear. The default is smoother = FALSE. This option also affects the residual-leverage, location-scale, and residual plots if included in the same panel.

# Creates an interactive index plot of the residuals
resid_interact(tree_model, plots = "index")

# Creates an interactive index plot with a smoother
resid_interact(tree_model, plots = "index", smoother = TRUE)

lev Residual-Leverage Plot

The option plots = "lev" creates an interactive residual-leverage plot. The cursor can be hovered over a data point to see a tooltip that contains the leverage, the standardized residual, the observed variable values, and the observation number of the data points. This plot is only available for “lm” and “glm” models.

The smoother option in resid_interact is also available for the residual-leverage plot. It indicates whether or not to include a loess smoother on the plot. Set smoother = TRUE to have the smoother appear. The default is smoother = FALSE. This option also affects the index, location-scale, and residual plots if included in the same panel.

# Creates an interactive residual-leverage plot
resid_interact(tree_model, plots = "lev")

# Creates an interactive residual-leverage plot with a smoother
resid_interact(tree_model, plots = "lev", smoother = TRUE)

ls: Location-Scale Plot

The option plots = "ls" creates an interactive location-scale plot. The cursor can be hovered over a point to see a tooltip that contains the prediction, the square root of the absolute value of the standardized residual, the observed values of the variables in the model, and the observation number of the point. This plot is only available for “lm” and “glm” models.

The smoother option in resid_interact is also available for the location-scale plot. It indicates whether or not to include a loess smoother on the plot. Set smoother = TRUE to have the smoother appear. The default is smoother = FALSE. This option also affects the index, residual-leverage, and residual plots if included in the same panel.

# Creates an interactive location-scale plot
resid_interact(tree_model, plots = "ls")

# Creates an interactive location-scale plot with a smoother
resid_interact(tree_model, plots = "ls", smoother = TRUE)

qq: Normal Quantile Plot

The option plots = "qq" creates an interactive normal quantile plot. When the cursor is hovered over a point, a tooltip appears that displays the theoretical value, the sample quantile, the observed data values, and the observation number of the point.

resid_interact contains the same option of qqline that is included with resid_panel. It indicates whether to include a 1-1 line on the qq-plot. If TRUE is specified, the line is included. By default, qqline = TRUE. The option of qqbands that is included with resid_panel has not been implemented in plotly, so it is not available as an option with resid_interact.

# Creates an interactive normal quantile plot
resid_interact(tree_model, plots = "qq")

# Creates a normal quantile plot with the 1-1 line removed
resid_interact(tree_model, plots = "qq", qqline = FALSE)

resid: Residual Plot

The option of plots = "resid" creates an interactive residual plot. When the cursor is hovered over a point, a tooltip appears that contains the prediction, the residual, the observed variable values, and the observation number associated with the point.

The smoother option in resid_interact is also available for the residual plot. It indicates whether or not to include a loess smoother on the plot. Set smoother = TRUE to have the smoother appear. The default is smoother = FALSE. This option also affects the index, residual-leverage, and location-scale plots if included in the same panel.

# Creates an interactive residual plot
resid_interact(tree_model, plots = "resid")

# Creates the residual plot with a smoother
resid_interact(tree_model, plots = "resid", smoother = TRUE)

yvp: Response vs. Predicted Plot

The option of plots = "yvp" creates an interactive plot of the response variable versus the predicted value. If the cursor is hovered over a point, a tooltip appears that contains the predicted value, the response variable value, the observed variable values, and the observation number.

# Creates an interactive residual vs. predicted value plot
resid_interact(tree_model, plots = "yvp")

all: Panel of All Plots

The option of plots = "all" creates an interactive version of the panel of all plots included in the package that are available for the type of model input into resid_interact.

# Creates an interactive panel of all plots available for an "lm" model
resid_interact(tree_model, plots = "all")

default: Default Panel

The option of plots = "default" creates an interactive version of the default panel of plots. That is, this is the panel that is created if no plots option is specified in resid_interact.

# Creates an interactive default panel with the option explicitly specified
resid_interact(tree_model, plots = "default")

R: Base R Inspired Panel of Plots

The option of plots = "R" creates an interactive version of the R panel of plots. This option can only be used with an “lm” or “glm” model.

# Creates an interactive version of the R panel of plots with the smoother option set to TRUE
resid_interact(tree_model, plots = "R", smoother = TRUE)

SAS: SAS Inspired Panel of Plots

The option of plots = "SAS" creates an interactive version of the SAS panel.

# Creates an interactive version of the SAS panel of plots
resid_interact(tree_model, plots = "SAS")